Lamar Odom Will Move to a Rehabilitation Center in Los Angeles to Continue Recovery

The 35-year-old basketball star is moving to a rehabilitation center in Los Angeles to continue his recovery, multiple sources tell ET, although it is not known when the transfer will take place. Lamar is currently at Sunrise Hospital in Las Vegas, where he's been since last Tuesday after he was found unconscious at the Love Ranch brothel in Crystal, Nevada.

“Everyone is waiting for the doctors word right now but Lamar will be returning to L.A. for further treatment," a source tells ET. "It will all be based on when he gets stronger and stabilized, but we are looking at a matter of days."

Lamar's condition is continuing to show positive signs, with a source telling ET he is now breathing on his own and is "alert and stable." We're also being told he is completely off a ventilator, and has even been able to say a few words.

But it's important to note that Lamar is still considered to be in critical condition. Despite a report that Lamar was helped out of his hospital bed and was assisted in moving to a chair, a source close to the family tells ET he did not leave his hospital bed, but did get up. However, he's "still very weak." In addition, he's currently receiving dialysis treatment after experiencing kidney failure.

"He is showing improvement in his condition, however, regaining complete organ function continues to be a top medical priority," the source says.

Lamar is going to need "a lot" of rehab in the coming months, E! News reports, and though a CT scan reportedly came back clean, there may be some cognitive issues in the future. But Lamar also passed a swallowing test -- a promising sign of neurological function -- and has communicated using hand signals.

A spokesperson for Lamar's aunt, JaNean Mercer, previously told ET that the NBA star had opened his eyes and was able to communicate on Friday, after being placed into a medically induced coma on Wednesday. When his doctor asked how he was doing, Lamar gave a thumbs up and responded, "Good morning."

"Lamar has always been blessed with a tenacious, fighting spirit, overcoming insurmountable obstacles to achieve the impossible," Mercer told ET on Monday. "These past few days have been no different. He is defying the odds in his toughest battle to date with God's grace."

"Each day Lamar is getting stronger and reaching significant milestones in his recovery," she continued. "We are committed to remaining by his side as a family for our champion, who we love immensely."